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Question
\mu=\frac{m}{l}
Function
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\text{Find the first partial derivative with respect to }m
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\text{Find the first partial derivative with respect to }l
\frac{\partial \mu}{\partial m}=\frac{1}{l}
Simplify
\mu=\frac{m}{l}
\text{Find the first partial derivative by treating the variable }l\text{ as a constant and differentiating with respect to }m
\frac{\partial \mu}{\partial m}=\frac{\partial}{\partial m}\left(\frac{m}{l}\right)
\text{Use differentiation rule }\frac{\partial}{\partial x}\left(\frac{f(x)}{g(x)}\right)=\frac{\frac{\partial}{\partial x}(f(x))\times g(x)-f(x)\times \frac{\partial}{\partial x}(g\left(x)\right)}{\left(g(x)\right)^2}
\frac{\partial \mu}{\partial m}=\frac{\frac{\partial}{\partial m}\left(m\right)l-m\times \frac{\partial}{\partial m}\left(l\right)}{l^{2}}
\text{Use }\frac{\partial}{\partial x} x^{n}=n x^{n-1}\text{ to find derivative}
\frac{\partial \mu}{\partial m}=\frac{1\times l-m\times \frac{\partial}{\partial m}\left(l\right)}{l^{2}}
\text{Use }\frac{\partial}{\partial x}(c)=0\text{ to find derivative}
\frac{\partial \mu}{\partial m}=\frac{1\times l-m\times 0}{l^{2}}
Any expression multiplied by 1 remains the same
\frac{\partial \mu}{\partial m}=\frac{l-m\times 0}{l^{2}}
Any expression multiplied by 0 equals 0
\frac{\partial \mu}{\partial m}=\frac{l-0}{l^{2}}
Removing 0 doesn't change the value,so remove it from the expression
\frac{\partial \mu}{\partial m}=\frac{l}{l^{2}}
Solution
More Steps
Evaluate
\frac{l}{l^{2}}
\text{Use the product rule }\frac{a^{n}}{a^{m}}=a^{n-m}\text{ to simplify the expression}
\frac{1}{l^{2-1}}
Reduce the fraction
\frac{1}{l}
\frac{\partial \mu}{\partial m}=\frac{1}{l}
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Solve the equation
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\text{Solve for }l
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\text{Solve for }m
l=\frac{m}{\mu }
Evaluate
\mu =\frac{m}{l}
Swap the sides of the equation
\frac{m}{l}=\mu
Cross multiply
m=l\mu
Simplify the equation
m=\mu l
Swap the sides of the equation
\mu l=m
Divide both sides
\frac{\mu l}{\mu }=\frac{m}{\mu }
Solution
l=\frac{m}{\mu }
Show Solutions
